Mechanical Design of a Novel Functionally Graded Lattice Structure for Long Bone Scaffolds
Abstract
1. Introduction
2. Materials and Methods
2.1. Design of TAOR Strucures
2.2. Euler–Bernoulli Beam Theory
2.3. Finite Element Model
3. Results and Discussion
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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D [mm] | L [mm] | l [mm] | W [mm] | |
---|---|---|---|---|
TAOR specimen | 5 | 35 | 15 | 150 |
ρ*/ρs [%] | D [mm] | d [mm] | a [mm] | |
---|---|---|---|---|
FS_10% * | 10 | 5 | 0.430 | 1.463 |
FS_20% | 20 | 5 | 0.646 | 1.157 |
FS_30% | 30 | 5 | 0.846 | 0.875 |
FS_40% | 40 | 5 | 1.063 | 0.568 |
HS_10% ** | 10 | 5 | 0.430 | 1.463 |
HS_20% | 20 | 5 | 0.646 | 1.157 |
HS_30% | 30 | 5 | 0.846 | 0.875 |
HS_40% | 40 | 5 | 1.063 | 0.568 |
ρ*/ρs Mean [%] | Density Gradient [%] | ρ*/ρs Inner Ring [%] | ρ*/ρs Outer Ring [%] | |
---|---|---|---|---|
FS_10%_FG | 10 | 5 | 11 | 6 |
FS_20%_FG | 20 | 5 | 21 | 16 |
FS_30%_FG | 30 | 5 | 31 | 26 |
FS_40%_FG | 40 | 5 | 41 | 36 |
HS_10%_FG | 10 | 5 | 12 | 7 |
HS_20%_FG | 20 | 5 | 22 | 17 |
HS_30%_FG | 30 | 5 | 32 | 27 |
HS_40%_FG | 40 | 5 | 42 | 37 |
Ring | D [mm] | d [mm] | a [mm] | |
---|---|---|---|---|
FS_10%_FG | 1 | 5 | 0.454 | 1.429 |
2 | 5 | 0.424 | 1.471 | |
3 | 5 | 0.380 | 1.534 | |
4 | 5 | 0.325 | 1.611 | |
FS_20%_FG | 1 | 5 | 0.667 | 1.128 |
2 | 5 | 0.641 | 1.165 | |
3 | 5 | 0.606 | 1.214 | |
4 | 5 | 0.564 | 1.273 | |
FS_30%_FG | 1 | 5 | 0.866 | 0.846 |
2 | 5 | 0.841 | 0.882 | |
3 | 5 | 0.806 | 0.931 | |
4 | 5 | 0.766 | 0.988 | |
FS_40%_FG | 1 | 5 | 1.088 | 0.532 |
2 | 5 | 1.057 | 0.576 | |
3 | 5 | 1.016 | 0.634 | |
4 | 5 | 0.971 | 0.698 | |
HS_10%_FG | 1 | 5 | 0.477 | 1.396 |
2 | 5 | 0.353 | 1.572 | |
HS_20%_FG | 1 | 5 | 0.686 | 1.101 |
2 | 5 | 0.585 | 1.244 | |
HS_30%_FG | 1 | 5 | 0.887 | 0.817 |
2 | 5 | 0.786 | 0.959 | |
HS_40%_FG | 1 | 5 | 1.114 | 0.496 |
2 | 5 | 0.994 | 0.665 |
Zone | Maximum Tensile Stress [MPa] | Maximum Compression Stress [MPa] | Deflection [mm] | |
---|---|---|---|---|
2 elements | 1 | 22.3 | 62.2 | 0.06334 |
2 | 9.754 | 18.173 | ||
4 elements | 1 | 22.4 | 62.5 | 0.06336 |
2 | 9.770 | 18.214 | ||
6 elements | 1 | 22.5 | 62.8 | 0.06347 |
2 | 9.773 | 18.227 | ||
8 elements | 1 | 22.6 | 63.0 | 0.06352 |
2 | 9.776 | 18.236 |
Elastic Modulus E [GPa] | Poisson’s Ratio ν | Density ρ [kg/m3] | |
---|---|---|---|
Ti6Al4V | 110 | 0.34 | 4430 |
Steel | 210 | 0.3 | 7850 |
Elastic Modulus E [GPa] | Poisson’s Ratio ν | |
---|---|---|
Shell | 2.85 | 0.363 |
Core | 0.596 | 0.3 |
δ 3 pbs [mm] | δ 4 pbs [mm] | |
---|---|---|
BS | 0.05492 | 0.04715 |
FS_bulk | 0.00216 | 0.00150 |
HS_bulk | 0.00256 | 0.00177 |
FS_10% | 0.22390 | 0.15180 |
FS_20% | 0.06347 | 0.04410 |
FS_30% | 0.03152 | 0.02202 |
FS_40% | 0.01921 | 0.01341 |
HS_10% | 0.31870 | 0.21820 |
HS_20% | 0.08772 | 0.06133 |
HS_30% | 0.04195 | 0.02945 |
HS_40% | 0.02460 | 0.01726 |
FS_10%_FG | 0.22380 | 0.15190 |
FS_20%_FG | 0.06301 | 0.04375 |
FS_30%_FG | 0.03135 | 0.02188 |
FS_40%_FG | 0.01908 | 0.01330 |
HS_10%_FG | 0.32260 | 0.22160 |
HS_20%_FG | 0.08795 | 0.06157 |
HS_30%_FG | 0.04198 | 0.02951 |
HS_40%_FG | 0.02446 | 0.01715 |
δ 3 pbs TI [mm] | δ 3 pbs EB [mm] | δ 3 pbs FEM [mm] | δ 4 pbs TI [mm] | δ 4 pbs EB [mm] | δ 4 pbs FEM [mm] | |
---|---|---|---|---|---|---|
FS_bulk | 0.00207 | 0.00151 | 0.00216 | 0.00132 | 0.00104 | 0.00150 |
HS_bulk | 0.00232 | 0.00157 | 0.00256 | 0.00146 | 0.00108 | 0.00177 |
C 3pbt | n 3pbt | R2 3pbt | C 4pbt | n 4pbt | R2 4pbt | |
---|---|---|---|---|---|---|
FS | 0.58 | 1.77 | 0.999 | 0.57 | 1.73 | 1.00 |
HS | 0.57 | 1.85 | 1.00 | 0.55 | 1.80 | 0.999 |
FS_FG | 0.59 | 1.78 | 0.999 | 0.58 | 1.74 | 0.999 |
HS_FG | 0.58 | 1.86 | 1.00 | 0.56 | 1.82 | 0.999 |
10% | 20% | 30% | 40% | 10%_FG | 20%_FG | 30%_FG | 40%_FG | |
---|---|---|---|---|---|---|---|---|
EIEB FS/EIEB HS 3 pbt | 1.42 | 1.38 | 1.33 | 1.28 | 1.44 | 1.40 | 1.34 | 1.28 |
EIEB FS/EIEB HS 4 pbt | 1.42 | 1.39 | 1.34 | 1.29 | 1.44 | 1.40 | 1.35 | 1.29 |
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Distefano, F.; Epasto, G.; Zojaji, M.; Ploeg, H.-L. Mechanical Design of a Novel Functionally Graded Lattice Structure for Long Bone Scaffolds. Designs 2025, 9, 62. https://doi.org/10.3390/designs9030062
Distefano F, Epasto G, Zojaji M, Ploeg H-L. Mechanical Design of a Novel Functionally Graded Lattice Structure for Long Bone Scaffolds. Designs. 2025; 9(3):62. https://doi.org/10.3390/designs9030062
Chicago/Turabian StyleDistefano, Fabio, Gabriella Epasto, Mahsa Zojaji, and Heidi-Lynn Ploeg. 2025. "Mechanical Design of a Novel Functionally Graded Lattice Structure for Long Bone Scaffolds" Designs 9, no. 3: 62. https://doi.org/10.3390/designs9030062
APA StyleDistefano, F., Epasto, G., Zojaji, M., & Ploeg, H.-L. (2025). Mechanical Design of a Novel Functionally Graded Lattice Structure for Long Bone Scaffolds. Designs, 9(3), 62. https://doi.org/10.3390/designs9030062